Home prices moved up at a torrid pace during the first half of the year, but don’t expect them to keep pace during the second half.

The big spike in mortgage rates over the past two months has reset the housing market and figures to take a bite out of demand at a time when more sellers have listed homes for sale and when price gains have tested investors’ purchasing appetites.

Mortgage rates, which stood at a low of 3.59% at the beginning of May, jumped to 4.58% during the last week of June, according to the Mortgage Bankers Association. Rates rose even more last Friday, after a strong jobs report firmed up investors’ expectations that the Federal Reserve would begin to curtail its bond-buying program later this year.

A rule of thumb holds that every one percentage point increase in interest rates reduces affordability by 10%, so the recent move in rates just made homes about 10% more expensive to buyers who need to finance their purchase.

“There’s no one in the business right now who doesn’t think the market hasn’t taken a step back. The evidence is all around us,” said Glenn Kelman, chief executive of real-estate brokerage Redfin. The number of Redfin customers who requested tours during the last week of June was down 5% from the average for the previous three weeks, while the number of customers making offers was down by 8% and the number of new customers edged down by 2%.

Here’s a look at seven areas to watch during the second half of 2013:

1. What will higher mortgage rates do to housing demand? Rates are now at their highest level in two years. For borrowers with less than a 5% down payment, the effective mortgage rate is at its highest level since mid-2009 because loans backed by the Federal Housing Administration now carry higher annual insurance premiums.

Economists say that even at a 4.5% or 5% mortgage rate, housing is still affordable by historical standards. Analysts at Bank of America Merrill Lynch note that prices would have to rise by 20% or rates would have to climb to around 6% before housing would look unaffordable. Also, they say that housing demand is shaped heavily by expectations of future affordability. That is, homeowners may be more eager to buy at a 4.5% mortgage rate when prices are rising than they were two years ago, when rates were lower but demand was soft because prices were falling.

But the bad news is that the level of rates may matter less than the speed of any increase. A sharp spike in interest rates—even to a level that is still historically low—represents a large payment shock to home shoppers. Many buyers shop for a home based on their monthly mortgage payment, which just shot up. The monthly payment on a $200,000 home with a 10% down payment just went up by $100 every month, almost a 13% increase. The monthly cost of a $450,000 home just went up by $250.

2. Don’t higher mortgage rates help in the short run by bringing more buyers off the fence? Not really. There’s little evidence that higher rates create new demand, even if they accelerate purchases from households that had already decided to purchase. Pending home sales in May rose sharply by 6.7% from April to their highest level in six years, but that spike could easily be reversed in June and July.

3. Who is knocked out of the market by rising rates? The jump in rates should be felt everywhere, but the entry market and the high-end market could see a bigger pinch. First-time buyers and others who were already stretching to qualify for a loan and scrape together the down payment could find themselves unable to buy the house they thought that they could back in April.

An entirely separate class of buyers—Mr. Kelman calls them “buyers of opportunity”—didn’t really need to buy a house, but they were willing to consider a $1-$2 million home-purchase back when rates were at 3.5%. Now, it may be less compelling, and these would-be buyers may simply spend money to renovate their existing residence.

4. What does this mean for investors? If anyone gains, it could be investors that have been buying up cheap homes as rental properties. “I see investors licking their chops,” said Redfin’s Mr. Kelman. “Investors were really getting frustrated this spring trying to compete against all this funny money” from low rates. Also, to the extent that rising rates freeze would-be buyers out of the market, that should help increase rental demand.

There have been signs, however, that higher home prices have prompted investors to dial back their purchases because it’s become more difficult to dig up bargains, even before rates began to rise.

5. How fast will inventory rise? Even before rates increased, the number of homes offered for sale was rising at a slightly faster pace than it normally does during the spring, even though inventory in May was still around 10% below last year’s level. One sign that inventory has picked up is that competitive offer situations are dropping. The share of offers written by Redfin agents that faced a competing offer fell to 69.5% of offers in May, down from 73.3% in April. One year ago, some 69.3% of offers faced at least one competing bid.

Markets that have seen larger increases in listings have seen even bigger declines in multiple-bid situations. In Orange County, Calif., where the inventory of homes for sale is up by more than one third since March, some 84% of homes where Redfin agents wrote an offer in May had competing bids, compared to 94% in April. In San Diego, some 73% of offers in May had multiple offers, compared to 87% in April.

6. Is this the end of the housing rebound? It depends on how much higher rates rise. For the last 18 months, home prices have shot up against a backdrop of fewer homes for sale—particularly distressed properties—and stronger demand. Housing bulls have argued that this recovery has been driven by fundamentals such as household formation, even if it has been accelerated by low rates. Bears have argued that the recovery has been mostly artificial, driven by cheap debt. The gyrations in bond markets are going to pull back the curtain on just how much the current recovery has depended on ultra-low mortgage rates.

The speed of national home-price gains in recent months—in the spring, various indexes showed they were rising by about 12% compared to one year ago—have stoked fears of a bubble. Rising mortgage rates are actually a positive, says John Burns, chief executive of John Burns Real Estate Consulting, because they should produce more sustainable price increases. “I don’t think it’s the end of price increases, but I think they’re going to moderate significantly,” he said.

7. When will we know how much rising rates have reset the market? New home sales will provide the first barometer of the impact on rates because they measure contracts signed. Still, they’ll be an imperfect gauge because many home builders are likely to buy down interest rates for buyers—something that many ordinary home sellers won’t be willing to do. Existing-home sales for June, which will be reported in two weeks, will show sales of many homes that went into contract in May, before the rate spike, so the true magnitude won’t be seen until next month’s report on July’s existing-home sales is released.

Any hit to home prices won’t show up for even longer. The Case-Shiller index is reported with a two-month delay, meaning that July prices won’t be reported until the end of September. Much of the price data out over the next two months won’t reflect the impact of rising rates.